From the Grammarist:
Doughnut vs. donut
The dictionary-approved spelling for the ring-shaped cake made of dough and fried in fat is doughnut. The shortened donut has been around since the late 1800s, but it wasnt popularized until the late 20th century, when the successful American doughnut chain Dunkin Donuts made it ubiquitous. Today, writers outside the U.S. still favor doughnut by a wide margin. Donut appears about a third of the time in published American writing.
Donut is a simpler spelling, so it may grow even more common now that it has a foothold. Those of us who dont wish to assist Dunkin Donutss branding would be wise to resist the trend, though.
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